Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using db = double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
void testCase() {
  ll n;
  cin >> n;
  for (int i = 1; i * i <= 2 * n; i++) {
    ll val = 2 * n - (i * (i + 1));
    ll dis = sqrt((val * 4) + 1);
    ll l = (-1 + dis) / 2;
    if (l > 0 && (i * (i + 1)) + (l * (l + 1)) == 2 * n) {
      cout << "YES"
           << "\n";
      return;
    }
  }
  cout << "NO"
       << "\n";
  return;
}
int main() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  testCase();
  return 0;
}